Does the set {\((1, 0)\), \((0, 1)\)} span \(\mathbb R^2\)? Explain.

Does the set {\((1, 2)\)} span \(\mathbb R^2\)? Explain.

Determine whether \((3, 7)\) lies in span(\((1, 2)\), \((0, 1)\)).

Determine whether \((1, 1, 1)\) lies in span(\((1, 0, 1)\), \((0, 1, 1)\)).

Find span(\((2, 0)\), \((0, 3)\)) as a subset of \(\mathbb R^2\).

Find a spanning set for the plane x + y + \(z=0\) in \(\mathbb R^3\).

Does {\((1, 0, 0)\), \((0, 1, 0)\)} span \(\mathbb R^3\)? If not, what does it span?

Show that {\((1, 0)\), \((1, 1)\)} spans \(\mathbb R^2\).

Find the span of {\((1, 2, 3)\), \((2, 4, 6)\)}.

A learner says three vectors always span \(\mathbb R^3\). Diagnose the error.